ABSTRACT Clustering is useful in elucidating associations among agents of networks and has been advantageously applied in numerous fields including biology, chemistry, sociology, and economics. Most clustering algorithms have been applied to (weighted) networks with a fixed topology. However, many networks are constructed to simulate particular dynamics on them; e.g., transmission of disease, vehicular transportation, electricity supply, and economic transfers in financial markets. These dynamics affect the large-scale structure that emerges from the underlying network. We present a clustering method that incorporates not only the weighted network topology, but also the particular dynamics for an application domain. The approach is general and can be used with any dynamic process that can be simulated on a network. We apply this method to several networks to validate it: a benchmark network, various toy networks, and two large realistic synthetic networks. These span four, five, and two orders of magnitude in numbers of agents and links, and average degree, respectively, and possess vastly different degree distributions. The largest network includes over 580,000 agents and 13 million edges. The results show that different structures arise from variations in dynamics processes for a fixed network, and reflect the changes in the process itself. We observe a sharp transition from unclustered to well-clustered communities as dynamical parameters vary.

[Show abstract][Hide abstract]ABSTRACT: Recent avian flu epidemics (A/H5N1) in Southeast Asia and case reports from around the world have led to fears of a human pandemic. Control of these outbreaks in birds would probably lead to reduced transmission of the avian virus to humans. This study presents a mathematical model based on stochastic farm-to-farm transmission that incorporates flock size and spatial contacts to evaluate the impact of control strategies. Fit to data from the recent epidemic in the Netherlands, we evaluate the efficacy of control strategies and forecast avian influenza dynamics. Our results identify high-risk areas of spread by mapping of the farm level reproductive number. Results suggest that an immediate depopulation of infected flocks following an accurate and quick diagnosis would have a greater impact than simply depopulating surrounding flocks. Understanding the relative importance of different control measures is essential for response planning.

[Show abstract][Hide abstract]ABSTRACT: Uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom [Proc. Natl. Acad. Sci. U.S.A. 104, 7327 (2007); Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008)], Blondel [J. Stat. Mech.: Theory Exp. (2008), P10008], and Ronhovde and Nussinov [Phys. Rev. E 80, 016109 (2009)] have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.

[Show abstract][Hide abstract]ABSTRACT: There has been considerable recent interest in algorithms for finding communities in networks--groups of vertices within which connections are dense, but between which connections are sparser. Here we review the progress that has been made towards this end. We begin by describing some traditional methods of community detection, such as spectral bisection, the Kernighan-Lin algorithm and hierarchical clustering based on similarity measures. None of these methods, however, is ideal for the types of real-world network data with which current research is concerned, such as Internet and web data and biological and social networks. We describe a number of more recent algorithms that appear to work well with these data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks.

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